How to use image sequence to control particles?
You are lucky more than me :) I got particles emitted only from a one frame (tested with 2.79, 2.83, 2.93 and according to this answer and its link to devs (also seen as closed bug report with this topic in 2017) ... seems like limitation persists. So what you see in your preview is a pure love of God :)
So ... seems like the only one option to control animation with texture is to translate animation into a gradient image.


To prevent release from black pixels I used image with transparency (PNGA). For some weird reason I had to set Alpha &gt; None to let it work as intended.
To get a bit of randomness of release apply a Noise filter on image



I know you said your example is just a prove of concept, but probably you would be able reuse for your needs as well.